We describe a new approach to relative p-adic Hodge theory based on systematic use of
Witt vector constructions and nonarchimedean analytic geometry in the style of both …

We introduce the notion of completed-local systems on the generic fiber of the formal
scheme and show that it gives an equivalence of categories. This generalizes the work of …

Nous étendons le théorème de presque-pureté de Faltings-Scholze-Kedlaya-Liu sur les
extensions étales finies d'algèbres perfectoïdes au cas des extensions ramifiées, sans …

We compute syntomic cohomology of semistable affinoids in terms of cohomology of (φ,
Γ)(φ, Γ)-modules which, thanks to work of Fontaine–Herr, Andreatta–Iovita, and Kedlaya …

These are extended and slightly1 revised notes from a four-lecture series at the 2017
Arizona Winter School on the topic of perfectoid spaces. The appendix describes the …

We develop the analog in equal positive characteristic of Fontaine's theory for crystalline
Galois representations of a p-adic field. In particular we describe the analog of Fontaine's …

Assume that, and let be a-adic discrete valuation ring with residue field admitting a finite-
basis, and let be a formally smooth formally finite-type-algebra.(Indeed, we allow slightly …

In their book, Rapoport and Zink constructed rigid analytic period spaces F^wa for Fontaine's
filtered isocrystals, and period morphisms from PEL moduli spaces of p-divisible groups to …

A dictionary between Fontaine-Theory and its analogue in equal characteristic Page 1 Journal
of Number Theory 129 (2009) 1734–1757 Contents lists available at ScienceDirect Journal of …

We establish a tilting equivalence for rational, homotopy-invariant cohomology theories
defined over non-archimedean analytic varieties. More precisely, we prove an equivalence …